Multi-dimensionality in the inner working of core-collapse supernovae has long been considered one of the most important ingredients to understand the explosion mechanism. We perform a series of numerical experiments to explore how rotation impacts the 3-dimensional hydrodynamics of core-collapse supernova. We employ a light-bulb scheme to trigger explosions and a three-species neutrino leakage scheme to treat deleptonization effects and neutrino losses from the neutron star interior. We find that the rotation can help the onset of neutrino-driven explosions for models in which the initial angular momentum is matched to that obtained from recent stellar evolutionary calculations (~ 0:3 - 3 rad s-1 at the center). For models with larger initial angular momenta, a shock surface deforms to be oblate due to larger centrifugal force. This makes a gain region, in which matter gains energy from neutrinos, more concentrated around the equatorial plane. As a result, the preferred direction of the explosion in 3-dimensional rotating models is perpendicular to the spin axis, which is in sharp contrast to the polar explosions around the axis that are often obtained from 2-dimensional simulations.

We examine the corecollapse times of isolated, two-mass-component star clusters using Fokker-Planck models. With initial condition of Plummer models, we find that the corecollapse times of clusters with M1/M2 >> 1 are well correlated with (N1/N2)^0.5 (m1/m2)^2 Trh, where (M1/M2) and (m1/m2) are the light to heavy component total and individual mass ratios, respectively, N1/N2 is the number ratio, and Trh is the initial half-mass relaxation time scale. We also find two-component cluster parameters that best match multi-component (thus more realistic) clusters with power-law mass functions.